Continuous Self-Avoiding Walk with Application to the Description of Polymer Chains

We develop the continuous self-avoiding walk (CSAW) methodology for investigating temperature dependent thermodynamic properties of finite polymer chains without imposing a lattice. This leads to a new concept:  the free energy theta temperature, T_(θF), at which the free energy is proportional to chain length. Above T_(θF), the polymer chain-solvent mixture leads to a single phase, whereas below T_(θF) the polymer solvent system has a positive surface tension with a tendency to phase separation to form a globular phase. For finite chains this coil-globule transition lies above the geometric theta temperature at which the distribution describes a Gaussian coil. CSAW provides the basis for a new approach to predict globular properties of real polymers.